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CHEE Measuring k l A in a Stirred-Tank Contactor It is difficult to determine both k l and A by experiment, as measuring interfacial area can be tedious if not impossible in some cases. However, the product k l A is more accessible. Mass transfer in a stirred tank can be quantified quite easily:  Equilibrate the system at low pressure under static conditions  Raise the reactor pressure several bar  At t=0, start the agitator and measure the amount of H 2 required to maintain constant pressure as a function of time. H2H2 1. Equilibrate at low P [H 2 ] = [H 2 low P low T 2. Raise P under static conditions [H 2 ] = [H 2 low P high T 3. Start agitator Maintain pressure [H 2 ]  [H 2 high P high T

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CHEE Measuring k l A in a Stirred-Tank Contactor When the agitator is started, transport of H 2 across the gas liquid interface commences, the rate of which is governed by: where n H2 is the number of moles of H 2 in the liquid phase. Dividing by the volume of liquid, V, yields an expression in terms of molar concentration: which can be integrated using the initial condition, t=0: [H 2 ] = [H 2 ] o to yield: which expresses the concentration of H 2 in the liquid phase as a function of time during the system’s approach towards equilibrium.

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CHEE Measuring k l A in a Stirred-Tank Contactor The integrated expression for the rate of physical adsorption of H 2 into a stirred solution: fits the experimental data quite well. The intensity of agitation, as measured by the stirring rate is seen to have a significant effect on the mass transfer rate.

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CHEE Whether a process operates under kinetic (chemical) control or mass transfer control depends on the rates of reaction and interfacial transfer. If our catalytic reaction is first order with respect to hydrogen: : mole/s m 3 and the rate of interfacial mass transfer (N H2 = F H2 /V) is: : mole/s m 3 then at steady state, these rates are equal, giving us: or Design Considerations